Transcript Asset Allocation - Villanova University

Chapter 5
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Summarize the function of strategic asset
allocation in portfolio management
Discuss the role of strategic asset allocation
in relation to exposures to systematic risk
Compare and contrast strategic and tactical
asset allocation
Appraise the importance of asset allocation
for portfolio performance
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Explain an advantage and a disadvantage of
implementing a dynamic versus a static approach to
strategic asset allocation
Discuss and interpret the specification of return and
risk objectives in relation to strategic asset allocation
Evaluate whether an asset class or set of asset classes
has been appropriately specified
Select and justify an appropriate set of asset classes for
an investor
Evaluate the theoretical and practical effects of
including an additional asset class such as inflationprotected securities, international developed markets or
emerging market securities, or alternative assets in an
asset allocation
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Formulate the major steps in asset allocation
Determine and justify a strategic asset allocation,
given an investment policy statement and capital
market expectations
Critique and revise a strategic asset allocation,
given an investment policy statement and capital
market expectations
Determine and justify tactical asset allocation (TAA)
adjustments to asset-class weights given a
description of a TAA strategy and expectational
data
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Integrated asset allocation
◦ capital market conditions
◦ investor’s objectives and constraints
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Strategic asset allocation
◦ constant-mix
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Tactical asset allocation
◦ mean reversion
◦ inherently contrarian
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Insured asset allocation
◦ constant proportion
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Strategic asset allocation combines investor’s
objectives and constraints with long-term
capital market expectations into IPSpermissible asset classes
Purpose is to satisfy investor’s objectives and
constraints
Process leads to a set of portfolio weights
called the policy portfolio
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Strategic asset allocation aligns portfolio’s
risk profile with investor’s objectives
Investors expect compensation for
accepting non-diversifiable (systematic) risk
Distinct asset classes have distinct risk
exposures
Strategic asset allocation effectively
controls systematic risk exposures
Strategic asset allocation also provides the
investor with a set of benchmarks for
appropriate asset mix and long-term risk
tolerance
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Strategic allocation sets investor’s longterm exposures to systematic risk
Tactical asset allocation (TAA) involves
short-term adjustments to asset weights
based on short-term predictions of relative
performance
TAA is an active and ongoing investment
discipline, whereas strategic asset
allocations are revisited only periodically or
when the investor’s circumstances change
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Some studies have indicated that asset
allocation explains the vast majority of
portfolio returns, far outweighing timing
and security selection
Cross-sectional studies have shown asset
allocation to explain much less (though still
a very significant amount) of portfolio
returns
However, other studies have shown that the
dispersion of results can vary more due to
security selection than asset allocation, and
thus indicate that skillful investors would
gain more from security selection
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Selecting an allocation method depends
on:
◦ Perceptions of variability in the client’s
objectives and constraints
◦ Perceived relationship between the past and
future capital market conditions
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importance of asset allocation
◦ Does Asset Allocation Policy Explain 40, 90, or
100 Percent of Performance?
◦ Ibbotson and Kaplan FAJ Jan/Feb 2000
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Asset/Liability Management (ALM) models
future liabilities and adopts an asset allocation
best suited to funding those liabilities
Asset-only approach does not explicitly model
liabilities
Dynamic Approach
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Static Approach
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◦ Asset allocation, actual returns and liabilities in one
period directly affect the optimal decision for the
following period
◦ Does not consider links between time periods
◦ Less costly and complex to model and implement
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Return objective
◦ Qualitative objectives describe fundamental goals
◦ Quantitative objectives specify return needed to achieve
goals
◦ Compounding must be considered through geometric
return and multiplicative rather than additive formulations
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Risk objective
◦ Qualitative (below average or above average)
◦ Quantitative
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numerical risk aversion measured through interview
Acceptable level of volatility
Shortfall/downside risk
Safety-first criterion
Behavioral biases
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Assets within a class should be relatively
homogeneous
Asset classes should be mutually exclusive
Asset classes should be diversifying
Asset classes as a group should comprise
the majority of world investable wealth
Asset class should have the capacity to
absorb a significant fraction of the
investor’s portfolio without compromising
liquidity
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domestic common equity
domestic fixed income
international common equity
international fixed income
real estate
cash and cash equivalents
others to consider:
◦ alternative – real estate often considered part of this
along with private equity, commodities, currencies, and
investment strategies of hedge funds
◦ TIPS
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Assets should be considered in a portfolio if
they improve the portfolio’s mean-variance
efficient frontier
This occurs if the asset class Sharpe ratio
exceeds the product of the existing portfolio’s
Sharpe ratio and the correlation between the
asset class return and the portfolio’s return
For example, an asset with a Sharpe ratio of
0.2 and a correlation of 0.9 to the return of a
portfolio with a Sharpe ratio of 0.15 should be
added because 0.2 > 0.15(0.9) = 0.135
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Investor Specific
◦ Consider investor’s net worth and risk attitudes
◦ Apply a risk tolerance function
◦ Determine the investor’s risk tolerance
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Capital Market Situation
◦ Identify capital market conditions
◦ Implement a prediction procedure
◦ Generate expected returns, risks and correlations
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Combined Investor-Market Relationship
◦ Use an optimizer to determine allocation given investor’s
risk tolerance
◦ Select asset mix
◦ Actual returns determine feedback for process
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As an investor you want to maximize the
returns for a given level of risk.
Your portfolio includes all of your assets and
liabilities
The relationship between the returns for
assets in the portfolio is important.
A good portfolio is not simply a collection of
individually good investments.
Given a choice between two assets
with equal rates of return, most
investors will select the asset with
the lower level of risk.
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Many investors purchase insurance for: Life,
Automobile, Health, and Disability Income.
The purchaser trades known costs for
unknown risk of loss
Yield on bonds increases with risk
classifications from AAA to AA to A….
Risk preference may have to do with amount
of money involved - risking small amounts,
but insuring large losses
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Quantifies risk
Derives the expected rate of return for a
portfolio of assets and an expected risk
measure
Shows that the variance of the rate of return
is a meaningful measure of portfolio risk
Derives the formula for computing the
variance of a portfolio, showing how to
effectively diversify a portfolio
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For an individual asset - sum of the potential
returns multiplied with the corresponding
probability of the returns
For a portfolio of investments - weighted
average of the expected rates of return for
the individual investments in the portfolio
Standard Deviation
( ) 
n
 [R
i 1
2
i
- E(R i )] Pi
For two assets, i and j, the covariance of
rates of return is defined as:
Covij = sum{[Ri - E(Ri)] [Rj - E(Rj)]pi}
 Correlation coefficient varies from -1 to
+1

rij 
Covij
 i j
 port 
n
w 
i 1
2
i
n
2
i
n
  w i w j Cov ij
i 1 i 1
where :
 port  the standard deviation of the portfolio
Wi  the weights of the individual assets in the portfolio, where
weights are determined by the proportion of value in the portfolio
 i2  the variance of rates of return for asset i
Cov ij  the covariance between the rates of return for assets i and j,
where Cov ij  rij i j
E(R)
0.20
0.15
0.10
0.05
With two perfectly
correlated assets, it
is only possible to
create a two asset
portfolio with riskreturn along a line
between either
single asset
2
Rij = +1.00
1
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
0.20
0.15
0.10
f
g
2
With uncorrelated
h
assets it is possible
i
j
to create a two
Rij = +1.00
asset portfolio with
k
lower risk than
1
either single asset
Rij = 0.00
0.05
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R)
0.20
0.15
0.10
f
g
2
With correlated
h
assets it is possible
i
j
to create a two
Rij = +1.00
asset portfolio
k
Rij = +0.50
between the first
1
two curves
Rij = 0.00
0.05
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
E(R) With
0.20 negatively
correlated
assets it is
0.15
possible to
create a two
0.10 asset portfolio
with much
0.05 lower risk than
either single
asset
Rij = -0.50
f
2
g
h
j
k
i
Rij = +1.00
Rij = +0.50
1
Rij = 0.00
-
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
Exhibit 7.13
E(R)
0.20
Rij = -0.50
Rij = -1.00
f
2
g
h
0.15
0.10
0.05
-
j
k
i
Rij = +1.00
Rij = +0.50
1
Rij = 0.00
With perfectly negatively correlated
assets it is possible to create a two asset
portfolio with almost no risk
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12
Standard Deviation of Return
Figure 8.9
E(R)
Efficient
Frontier
A
B
C
Standard Deviation of Return
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The efficient frontier represents set of
efficient portfolios at various levels of risk
◦ part of the minimum variance frontier which
represents portfolio with the smallest variance of
return for its level of expected return
◦ MVF has a global minimum variance portfolio which
is the smallest variance of all minimum variance
portfolios
◦ represents feasible set of investment opportunities
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find an efficient portfolio with combination of
risk and return that is appropriate for investor
◦ use mean-variance optimization (or other processes
to determine asset class weights)
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Investors should choose from efficient portfolios
consistent with the investor’s risk tolerance
Unconstrained: asset class weights must sum to
one
Sign-constrained: no short sales (negative
weights)
quality of inputs
◦ recommended asset allocations are highly sensitive to
small changes in inputs
 estimation error in expected returns is about 10 times as
important as estimation error in variances and 20 times as
important as estimation error in correlation (covariance)
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Capital market theory extends portfolio theory
and develops a model for pricing all risky assets
Capital asset pricing model (CAPM) is early
attempt at determining the required rate of
return for any risky asset
◦ problems with this model in part due to unrealistic
assumptions
◦ current research attempts to find “true” asset pricing
model but no one accepted model
◦ concepts from CAPM used in practice even though model
has problems
 for example, beta as a measure of systematic risk
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An asset with zero variance
Zero correlation with all other risky assets
Provides the risk-free rate of return (RFR)
Will lie on the vertical axis of a portfolio
graph
asset class of cash and cash equivalents
Covariance between two sets of expected returns is
n
Cov ij   [R i - E(R i )][R j - E(R j )] / n *
i 1
*instead of (/n), multiply by probability if calculating covariance of expected returns
Because the returns for the risk free asset are certain,
 RF  0
Thus Ri = E(Ri), and Ri - E(Ri) = 0
Consequently, the covariance of the risk-free asset with any risky asset or
portfolio will always equal zero. Similarly the correlation between any risky
asset and the risk-free asset would be zero.
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Under CAPM, in equilibrium each asset has
nonzero proportion in M
All assets included in risky portfolio M
◦ All investors buy M
◦ If M does not involve a security, then nobody is
investing in the security
◦ If no one is investing, then no demand for
securities
◦ If no demand, then price falls
◦ Falls to point where security is attractive and
people buy and so it is in M
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CML represents new EF
◦ all investors have the same EF but choose different
portfolios based on risk tolerances (with
homogeneous investors - assumption of CMT)
◦ investor spreads money among risky assets in
same relative proportions and then borrows/lends
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separation theorem
◦ optimal combination of risky assets for investor
can be determined without knowledge of
investor’s preferences toward risk and return
 investment decision
 financing decision
The decision of both investors is to invest in
portfolio M along the CML (the investment
decision)
E ( R port )
CML
B
M
A
PFR
 port
Standard Deviation of Return
Figure 9.3
Unsystematic
(diversifiable)
Risk
Total
Risk
Standard Deviation of
the Market Portfolio
(systematic risk)
Systematic Risk
Number of Stocks in the Portfolio
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The existence of a risk-free asset resulted
in deriving a capital market line (CML) that
became the relevant frontier
An asset’s covariance with the market
portfolio is the relevant risk measure
This can be used to determine an
appropriate expected rate of return on a
risky asset - the capital asset pricing model
(CAPM)
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The relevant risk measure for an individual
risky asset is its covariance with the market
portfolio (Covi,m)
This is shown as the risk measure
The return for the market portfolio should be
consistent with its own risk, which is the
covariance of the market with itself - or its
variance:
 m2
In equilibrium, all assets and all portfolios
of assets should plot on the SML
Any security with an estimated return that
plots above the SML is underpriced
Any security with an estimated return that
plots below the SML is overpriced
A superior investor must derive value
estimates for assets that are consistently
superior to the consensus market
evaluation to earn better risk-adjusted
rates of return than the average investor
Stability of Beta
Comparability of Published Estimates of Beta
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Number of observations and time interval used in
regression vary
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Value Line Investment Services (VL) uses weekly rates of
return over five years
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Merrill Lynch (ML) uses monthly return over five years
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There is no “correct” interval for analysis
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Weak relationship between VL & ML betas due to
difference in intervals used
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Interval effect impacts smaller firms more
Market portfolio
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Specify the risk in microeconomic terms
using certain characteristics of the
underlying sample of securities
( Rit  RFRt )  ai  bi1 ( Rmt  RFRt )  bi 2 SMBt  bi3 HMLt  eit
extension of Fama-French 3-factor model includes a fourth factor that
that accounts for firms with positive past return to produce positive
future return - momentum
( Rit  RFRt )  ai  bi1 ( Rmt  RFRt )  bi 2 SMBt  bi3 HMLt  bi 4 PR1YRt  eit
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60/40 stock/bond asset allocation is
appropriate or at least a starting point for an
average investor’s asset allocation
the allocation to bonds should increase with
increasing risk aversion
investors with longer time horizons should
increase their allocation to stocks
a rule-of-thumb for the % allocation to
equities is 100 minus the age of the investor
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implementation choices
◦ investment approach and instruments to execute
 passive
 tracking portfolio of securities – self-managed, ETF or fund designed to replicate returns of broad index
 cash plus long position in either swap or futures for
particular asset class
 active
 portfolio reflecting investor’s perceived special insights or
skills with no attempt to track any broad index
 derivatives-based position that reflects active investing ideas
 semi-active (enhanced indexing)
 tracking portfolio that permits some under- or overweighting of securities relative to the index but with
controlled tracking risk
 derivatives-based position in asset class along with some
controlled active risk mgt (i.e., actively managing duration)
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implementation choices
currency risk management decisions
◦ need to decide what part of exposures to hedge
 passively manage
 actively manage
 currency overlay manager
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rebalancing to target weights
◦ calendar basis
◦ percentage-of-portfolio basis
 rebalancing threshold / trigger point
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Taxable
Human capital – present value of future income
– must be considered but is not readily
tradable
◦ Safer labor income permits a higher equity allocation
◦ Human capital correlations with stock market
(stockbrokers, etc) should result in lower equity
allocations
◦ Labor flexibility should permit higher equity
allocations
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Mortality risk – family loses human capital with
early death – can be hedged with insurance
Longevity risk – outlive assets in retirement –
annuity products help reduce this risk
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Active management at the asset class level
Often takes place after strategic allocation
decision but before decisions on managing
specific asset classes
Overlay strategy makes strategic allocations
and adjusts asset class weights using
derivatives
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Market prices explicitly describe the returns
available (cash yield approximates future
returns)
Relative expected returns reflect relative risk
perceptions
Markets are rational and mean reverting